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9th grade 2008 Russian Mathematical Olympiad 6th question

Source: All Russian 2008, Grade 9, Problem 6

May 21, 2008
geometrycircumcircletrigonometrysearchgeometry unsolved

Problem Statement

The incircle of a triangle ABCABC touches the side ABAB and ACAC at respectively at XX and YY. Let KK be the midpoint of the arc AB^\widehat{AB} on the circumcircle of ABCABC. Assume that XYXY bisects the segment AKAK. What are the possible measures of angle BACBAC?
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